Question

14. In the following figure, M is the midpoint of
(FA) and (MA) and (MB) are the tangents issued
from M to the circle(C).
F
M
B
(C)
question: Show that ABF is a right triangle.​

Answer 1

Answer:

angle OAM and OBM are right angles because tangents form right angles with radii.

AO=BO and MA=MB

Quadrilateral MAOB =360 degrees

so angles AOB and AMB=90 degrees each

angle MBF=90 degrees

M is the midpoint of FA so MA=MF

MB=MF

Triangle MBF is a right triangle because angle BMF is 90 degrees and  MB=MF